The equation to represent the given situation is 1/2X-5=11-5/6 using X as the variable.
What is an equation and how it can be formed?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
When we are given a mathematical problem that is or may be described using algebraic expressions, we form and solve equations. The information from the situation and the algebraic expressions can be used to create an equation. The equation can then be solved to obtain the answer.
Given the situation: If 5 is lessened by 1/2 of a number the result is the same as subtracting 5/6 from 11.
To write an equation for the given situation.
Let the number be X.
If 5 is lessened by 1/2 of the number, we get the expression 1/2X-5
Subtracting 5/6 from 11 gives the expression 11-5/6
Now, it is given that both the situations are same so equating both the expressions we get,
1/2X-5=11-5/6
⇒1/2X-5=61/6
Hence, the equation to represent the situation is 1/2X-5=11-5/6.
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The telephone company offers two billing plans for local calls. Plan 1 charges $23 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)
a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23
b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1
c. the number of monthly calls x is x > 100
What is inequality ?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Plan 1: $23 per month for unlimited calls
Plan 2: $19 per month + $0.04 per call
Let the number of calls be x
a. 19 +0.04x >23
0.04x >4
x > 100
b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.
On solving the above inequality, we get over 100 calls should be made so that Plan 1 is more economical than Plan 2.
c. x > 100
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Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?
We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
Given,
The quantity of medicine added to the original mixture = 15 ounces
New quantity of medicine in the mixture = 18 ounces
Quantity of water in the mixture = 7 ounces
Total new quantity of mixture = 18 + 7 = 25 ounces
Original quantity of medicine in the mixture = 18 - 15 = 3 ounces
Original quantity of water in the mixture = 7 ounces
Total original quantity of mixture = 3 + 7 = 10 ounces
We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.
Here,
Proportion of medicine and water in original mixture = 3:7
Quantity of medicine and water in new mixture = 18:7
Now,
18 ÷ 3 = 6
Then, 7 × 6 = 42
So, 42 - 7 = 35
Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
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Consider the set t = {1, 2, 3, 4, 5, 6}. let r = {(a, b) | a divides b} be a relation on the set t. the tabular representation for the ordered pairs of the given relation r on the set t is:_________
The ordered pairs of the given relation r on the set t is ungrouped data.
What is ungrouped data?The data you initially collect from an experiment or study is known as ungrouped data. The data is unsorted, unclassified, or otherwise grouped; it is therefore considered to be raw. A list of numbers is an ungrouped piece of data.
Ungrouped data is a distribution type where each piece of information is presented in its rawest form. For instance, a batsman's five most recent scores are 45, 34, 2, 77, and 80.
Raw data is another name for ungrouped data.
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Anyone know how to solve ?
1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x-2y = -16
Ographing
substitution
O elimination
distributive
(1 point)
Suppose a local office store has a press that can print 54,000 brochures per hour. How many brochures can be printed during a 3 1 4 hour run?
Answer:
Step-by-step explanation:
Rate: 54000 brochures per hour
Formula: D=RT Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)
Two ways
1. 54,000(3 1/4)=175,500
2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.
(54,000 x 314 = 16,956,000)
Hope this helps!
An electronic store has television sets marked down 30 percent. What is the total price of five television sets that regularly sell for $115.75, $218.95, $320.75, $125.65, and $221.75?
Answer:
why did the teacher give an exam
Complete the congruence statements for each pair of congruent figures below
Triangles are congruent if their matching interior angles and sides are all congruent.
What is congruence in math?
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Congruent figures: what are they?
Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.What is congruent shapes?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.Learn more about congruent
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please help with math homework
Using the Pythagorean Theorem, it is found that:
a) The hypotenuse is of 9.49 cm.
b) The new area of the triangle is of 30 cm².
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, the sides are given as follows:
3 cm and 9 cm.
Hence the hypotenuse is given by:
h² = 3² + 9²
h = sqrt(3² + 9²)
h = 9.49 cm.
The hypotenuse is of 9.49 cm.
What is the area of a right triangle?The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:
A = 0.5ab.
For this problem, we have that:
The side of 3 cm is increased by 2 cm, hence a = 5 cm.The side of 9 cm is increased by 3 cm, hence b = 12 cm.Then:
A = 0.5 x 5 x 12 = 30 cm².
The new area of the triangle is of 30 cm².
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Which equation below combines with the equation -4 x+6 y=3 to form a system with an infinite number of solutions?
A. 0.5+x=1.5 y
B. 0.75+2 x=1.5 y
C. 0.5+2 x=1.5 y
D. 0.75+x=1.5 y
To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.
A system of equations is a set of two or more equations which includes common variables.
To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.
Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).
-4x + 6y = 3 ⇒ 3 + 4x = 6y
To make 6y into 1.5y, divide both sides by 4.
3 + 4x = 6y ⇒ 0.75 + x = 1.5 y
Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.
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It is given that M is the midpoint of segment . Therefore by the definition of a midpoint. It is also given that Angles and are right angles. Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem, . Then, it follows that by the criteria. In congruent triangles, corresponding sides are congruent, thus . In conclusion by definition of congruent angles.
The congruency can also be tested by three postulates shown in the lesson: ASA (angle-side-angle), SAS (side-angle-side), and SSS (side-side-side). The first one claims that triangles are congruent if two angles and one side (between the angles) of one triangle are equal to two angles and one side of another triangle.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
A ∠ ≅ ∠ .
Vertical Angles Theorem: ...
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are congruent and supplementary, then each is a right angle.Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).
Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem.
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A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.
The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
The largest angle is twice the smaller angle minus 30 degrees.
The sum of the triangle's interior angles is x + y + z = 180.
Which two equations represent the remaining angle relationships?
Select each correct answer.
1) x=y−z+40
2) x=2z−30
3) x=y+z−40
4) x=30−2z
5) x = y + z + 40
The correct answer would be option 2 and 3:
2) x=2z−303) x=y+z−40How to solve for the anglesWe have to sove the problem by carefully trying to understand the statements
x = largest angle
y = next largest angle
z = smallest.
1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
largest angle < y + z
This would be represented as
x = y + z - 40
2. The largest angle is twice the smaller angle minus 30 degrees.
This is represented as
2 times of smallest = 2 * z = 2z
minus 30 degrees = 2z - 30
Hence the solutions to the question from the option that we have would be the options
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Answer:
2) x=2z−30
3) x=y+z−40
Step-by-step explanation:
with the steps as well please
Answer:
Step-by-step explanation:
(i)
[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]
(ii)
[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]
(iii)
[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]
A group of friends were working on a student film that had a budget of $1400. They
used 67% of their budget on props. How much money did they spend on props?
Answer:
That is wrong it is not $938 its $322
Step-by-step explanation:
Eddie used 9.6 cups of flour to bake 3 cakes. How much flour, on average, did he put in each cake?
Answer: i believe its 3.2 cups per cake
Step-by-step explanation:
9.6 / 3 = 3.2
Is -71 - 43 positive or negative?
Answer:
Negative
Step-by-step explanation:
what is the area of the triangle below
The area of triangle is 12 square units.
What is the triangle?
Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given:
The given points are
A=(1,2)
B=(1,8)
C=(5,2)
According to given question we have
By the use of distance formula , we get
[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]
Area of right triangle(A) is given by:
[tex]Area =\frac{1}{2} base *height[/tex]
where,
base of the triangle =4 units
height of the triangle =6 units.
[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]
Therefore, the area of triangle is 12 square units.
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STRUCTURE The students in Mrs. Mangione’s class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles. Select all that apply.
The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.
How to illustrate the information?When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:
= 2 × m
= 2m
The expression that represents the difference between the student's guess and the actual number of marbles will be:
= 1206 - 2m
= 2(603 - m)
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Find the geometric mean between pair of numbers.
3√5/4 and 5√5/4
The geometric mean of 3√5/4 and 5√5/4 is 5√3/4.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 3√5/4 and 5√5/4 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 3√5/4, and x2 = 5√5/4
GM = √(3√5/4)(5√5/4)
GM = √(75/16)
GM = 5√3/4
Hence, the geometric mean of 3√5/4 and 5√5/4 is 5√3/4.
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What types of things have you measured before?
Answer:
1. Room size (length * width) for carpet
2. From window top to floor for curtains
Step-by-step explanation:
Find the sum of pair of vectors. <6,-31> + (-22,3)
According to the given statement The sum of pair of vectors are = (-16 , -28).
What precisely is vector addition?The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.
According to the given data:Given two vectors are:
a =(6,-31)
b = (-22,3)
The vector sum is,
M = (a1 + b1, a2 + b2)
= (Mx, My).
Substitution of the value we get:
M = (6 + (-22), (-31) + (3))
= (-16 , -28)
The sum of pair of vectors are = (-16 , -28).
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Need as soon as possible please
Answer:
Just graph, first one Y int: 2 and X is rise over run 1 and 2
Step-by-step explanation:
Which of the following defines workplace politics?
O Choices made according to law
O Beliefs of a person or social group in which they have an emotional investment
O Games played in a workplace environment to achieve status, advancement and money
O Professional standards of conduct, based on moral principles and values, guilding decision-making and actions
Answer:
"Games played in a workplace environment to achieve status, advancement and money"
The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking. a. after how many weeks will the vasquez family both visit their grandmother and host the neighbor hood party? b. after how many weeks will all three events occur?
Using least common multiple (LCM), the Vasquez family both visit their grandmother and host the neighbor hood party after 24 weeks. After 48 weeks, all three events will occur at the same time.
A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.
If the Vasquez family visit their grandmother every 3 weeks and host a neighbor hood party every 8 weeks, to know when will these event will occur at the same time, solve for the LCM of 3 and 8.
3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .
8 : 8, 16, 24, 32, 40, . . .
LCM = 24
Hence, after 24 weeks, both will occur at the same time.
To know when will the three events will occur at the same time, solve for their LCM.
3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .
8 : 8, 16, 24, 32, 40, 48, . . .
16 : 16, 32, 48, . . .
LCM = 48
Hence, after 48 weeks, all three events will occur at the same time.
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Help wanted! Im I’m desperate need of assistance!
Answer:
-2/5
Step-by-step explanation:
Hi there!
We find slope by using rise over run.
For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).
[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]
You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).
[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]
2/-5 is the same as -2/5, so that is your answer
Which statements prove that m || n?
Answer:
The first 2 and the 2nd to last equations
Step-by-step explanation:
Angles 8 and 10 are alternate interiors, which would only work if m and n are parallel.
Angles 1 and 9 are congruent angles, which would only work if m and n are parallel.
Angle 1 and 3 are on the same line, so that can't prove it.
m8 and m9 could only add up to 180 if m and n are parallel, which makes this also true.
Angles 7 and 10 add up to 180, but can't be congruent.
what is a non-repeating decimal, give examples of nom repeating decimals.
Answer:
Recurring Decimal
Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).
Examples are
0.6666666666,
1.456456456
Step-by-step explanation:
Set as brainliest
PLEASE PLEASE PLEASE HELP!! ASAP!! BRAINLIEST FOR WORK THAT SHOWS ALL STEPS AND CORRECT ANSWERS!! :)
1. Factor the expression: x^6–729. Show your work for full credit.
2. Solve the equation 2x^2+16x–11= -7 by completing the square. Show your work for full credit.
3. Factor over the complex numbers. Show your work for full credit. x^4–5x^2–36
1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18
3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)
How to factorize expressions?
1) We are given the expression; x⁶ - 729
It can also be written as;
(x²)³ - 9³
Now, from factorization of algebra, we know that;
a³ - b³ = (a - b)(a² + ab + b²)
Thus;
(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)
= (x² - 9)(x⁴ + 9x² + 81)
= (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.
Add 7 to both sides to get;
2x² + 16x – 11 + 7 = -7 + 7
2x² + 16x – 4 = 0
Divide through by 2 to get;
x² + 8x – 2 = 0
Add 2 to both sides to get;
x² + 8x = 2
Take half of the x term and square it and then add the result to both sides to get;
x² + 8x + 16 = 2 + 16
Rewrite the perfect square on the left to get;
(x + 4)² = 18
Take square root of both sides to get;
x + 4 = ±√18
Subtract 4 from both sides to get;
x = -4 ± √18
x = -4 + √18 or -4 - √18
3) We want to factorize x⁴ – 5x² – 36
Using the difference of squares identity, we know that;
a² - b² = (a + b)(a - b)
Thus;
x⁴ – 5x² – 36 = (x² + 9)(x² - 4)
Now, (x² + 9) factored over the complex numbers gives;
(x² + 9) = (x + 3i)(x - 3i)
Thus;
x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)
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What is line parallel to -x?
Answer:
I think its -y
Step-by-step explanation:
Answer:
x is my answer
Step-by-step explanation:
i don't know sorry
Two shops are selling the same DVD. In Tesco the DVD cost £11.49. In Asda the DVD
costs £13.99. Asda have an offer- "20% off all DVDs". Which shop should you buy the DVD
from?
